Bifurcation of solutions of $U(1)$-equivariant semilinear boundary value problems
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Published:2023-02-26
Issue:
Volume:
Page:1-10
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ISSN:1230-3429
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Container-title:Topological Methods in Nonlinear Analysis
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language:
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Short-container-title:TMNA
Author:
Pejsachowicz Jacobo
Abstract
Assuming that there is a known (trivial) branch of solutions of a parameterized family
of equations, topological bifurcation studies the topological invariants of the linearized equations along the trivial branch whose nonvanishing entails the
appearance of bifurcation from the trivial branch. We introduce here some refined topological invariants for semilinear elliptic boundary value problems equivariant
with respect to the action of the circle $U(1)$ allowing to improve, in this case,
some previously obtained bifurcation criteria for general nonlinear elliptic boundary value problems.
Publisher
Uniwersytet Mikolaja Kopernika/Nicolaus Copernicus University
Subject
Applied Mathematics,Analysis